InterviewSolution
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InterviewSolution
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`2 tan^(-1) (-2)` is equal toA. `-cos^(-1) ((-3)/(5))`B. `-pi + cos^(-1).(3)/(5)`C. `-(pi)/(2) + tan^(-1) (-(3)/(4))`D. `-pi + cot^(-1) (-(3)/(4))` |
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Answer» Correct Answer - A::B::C Let `tan^(-1) (-2) = theta " or " tan theta = -2` `rArr theta in (-pi//2, 0) " or " 2 theta in (-pi, 0)` `cos (-2 theta) = cos 2 theta = (1 - tan^(2) theta)/(1 + tan^(2) theta) = (-3)/(5)` or `-2 theta = cos^(-1) ((-3)/(5)) = pi - cos^(-1).(3)/(5)` or `2 theta = pi + cos^(-1).(3)/(5) = - pi + tan^(-1).(4)/(3)` `= - pi + cot^(-1).(3)/(4) = - pi + (pi)/(2) - tan^(-1). (3)/(4)` `= - (pi)/(2) - tan^(-1).(3)/(4) = - (pi)/(2) + tan^(-1) (-(3)/(4))` |
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